Math Answers

A population consist of the number 2,3,4

a. Enumerate all possible sample size of 2.

b. Compute for the mean of each sample.

c. Find tye mean of the mean.

d. Find the standard deviation of the sample means.

e. Find the population mean.

f. Find standard deviation.

g. Find the standard error of the mean

u( x, y) = e^x(xsiny+ycosy) find the differentials

What's poison distribution

Sprinters who run races involving curves around a track (usually distances over 200 meters) often have a preference for a particular lane. A runner might feel that an assignment to an outside lane places her at a disadvantage relative to her opponents. In fact, a 2001 survey of college-level sprinters found that 75% preferred to run in lane #4.

Consider this experiment. As a race organizer, you randomly select five runners from a pool of nine and assign them to lane #1, lane #2, lane #3, and so on, in the order they are selected.

How many experimental outcomes are there for this experiment? 

Let X follows a normal distribution with mean 40 and variance 9. Then mean of Y= (X-40)/3 is

        [ 1 0 -1

3. Consider the matrix A =  0 3 0

                      -1 0 1 ]

1. Find the eigenvalues of A.
2. Find the eigenspaces corresponding to each eigenvalue from A.

2. Consider a linear transformation T: R³ → R³ defined by

  ([x         [ x + 4y +3z  

T  y     =      -5y - 4z 

    z])        5x + 10y + 7z ]

Note: T is a 3x1 matrix containing x, y, z respectively. T is equal to another matrix as shown above.

a) Find the matrix A for T

b) Find a basis for ker(T) and the dim(ker(T)). Then find dim(Im(T)), without finding a basis for Im(T). (Show all working)

c) Find a basis for Im(T)

1. Answer the following questions

                                                              →            →            →  [ 1

a) Consider the linear transformation T(x) = proj_u(x), where u =  0

                                                                                                      3 ] 

Find the matrix for T.

b) Find the matrix for the linear transformation which reflects every vector in R² across the x-axis and then rotates every vector through an angle of 𝝅/6. (Show all working)

EXERCISE 2: Find the rank and the nullity of the linear transformation S: p_1→ℝ given by 

     S(p(x)) = ∫_0^1p(x)dx.